Abstract
This paper talks about generating the minimal surfaces which are subject to the well-known Plateau problem. The differential form of the Plateau problem is defined at first and, its associated discrete schemes which reduced from the finite element methods could be practically solved by the numerical iteration methods like the Newton's iteration. The convergence property of the finite element solutions are proved by steps and some multi-grid algorithms have been implemented to speed up the computation. These new approximation methods will be applied to the project of generating the minimal surfaces on computer softwares later.
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